help using matlab solve ga function for optimization of non linear expression

Hello , i have this non linear function called "h" shown in the code bellow.

I want to optimize k1, k2 ,a ,b parameters so this function will get values between 0.55 and 0.45 over the x axes.

I have tried to use the following manual and save the script file as optim.m

i tried to use use solve ga to get my function be get values between 0.55 and 0.45 over the x axes

https://www.mathworks.com/help/gads/ga-nonlinear-constraint-problem-based.html

i get an error shown bellow.

Where did i go wrong?

"Error using optim

Constraints must be an OptimizationConstraint or a struct containing OptimizationConstraints."

Thanks.

h=@(a,b,k1,k2)abs(a*exp(-j*k1*x)+b*exp(-j*k2*x));
cam=h(a,b,k1,k2);
prob = optimproblem("Objective",cam);

prob.Constraints.cons1=a<=1;
prob.Constraints.cons2=a>=-1;
prob.Constraints.cons3=b<=1;
prob.Constraints.cons4=b>=-1;
prob.Constraints.cons5=h<=0.55;
prob.Constraints.cons5=h>=0.45;
[sol,fval] = solve(prob,"Solver","ga");

Answer 1

[Matt J]

See, Optimize with Nonlinear Constraints Using GA. It should look something like this:

x=linspace(0,100,10000);

vars = ga(fun,4,A,b,Aeq,beq,lb,ub,  @(vars)nonlcon(vars,x),   options);

function [c,ceq]=nonlcon(vars,x)

 a=vars(1); b=vars(2);
 k1=vars(3); k2=vars(4);

 h =abs(a*exp(-j*k1*x)+b*exp(-j*k2*x));

 c(1)=0.45-min(h);
 c(2)=max(h)-0.55;

 ceq=[];
 
end

[fima v]

where di i go wrong in my example code in the post?

Thanks.

[Matt J]

Something like the following, perhaps.

a=optimvar('a','Lower',-1,'Upper',+1);
b=optimvar('b','Lower',-1,'Upper',+1);
k1=optimvar('k1',___);
k2=optimvar('k2',___);


h=@(a,b,k1,k2)abs(a*exp(-j*k1*x)+b*exp(-j*k2*x));
cam=fcn2optimexpr( h, a,b,k1,k2);

prob = optimproblem("Objective",cam);
prob.Constraints.camUpper=cam<=0.55;
prob.Constraints.camLower=cam>=0.45;

[sol,fval] = solve(prob,"Solver","ga");

[Matt J]

Or maybe,

a=optimvar('a','Lower',-1,'Upper',+1);
b=optimvar('b','Lower',-1,'Upper',+1);
k1=optimvar('k1',___);
k2=optimvar('k2',___);


h=@(a,b,k1,k2)abs(a*exp(-j*k1*x)+b*exp(-j*k2*x));
hmax=@(a,b,k1,k2) max(h(a,b,k1,k2));
hmin=@(a,b,k1,k2) min(h(a,b,k1,k2));

cam=fcn2optimexpr( h, a,b,k1,k2);
camMax=fcn2optimexpr( hmax, a,b,k1,k2);
camMin=fcn2optimexpr( hmin, a,b,k1,k2);

prob = optimproblem("Objective",cam);
prob.Constraints.camUpper=camMax<=0.55;
prob.Constraints.camLower=camMin>=0.45;

[sol,fval] = solve(prob,"Solver","ga");

[fima v]

Hello it gives me error regarding ___ of the line bellow?

what could be done?

Thanks

k1=optimvar('k1',___);

Error: File: solve.m Line: 3 Column: 18

Invalid text character. Check for unsupported symbol, invisible character, or pasting of non-ASCII

characters.

[Matt J]

You were meant to fill in the blank with appropriate arguments, or remove it if there are none.

[fima v]

Hello, it gives me the following error.

Why you created two functions of the same type.

|you have changed the original code.could you please use one "h" function?

i only want a simple example to run

Error using .*

Optimization variables cannot be combined with complex data.

Error in *

Error in solve>@(a,b,k1,k2)abs(a*exp(-j*k1*x)+b*exp(-j*k2*x)) (line 5)

h=@(a,b,k1,k2)abs(a*exp(-j*k1*x)+b*exp(-j*k2*x));

Error in fcn2optimexpr>createFunctionExpression (line 261)

[evalOut{:}] = func(evalInputs{:});

Error in fcn2optimexpr (line 120)

[varargout{1:nout}] = createFunctionExpression(func, ...

Error in solve (line 8)

cam=fcn2optimexpr(h,a,b,k1,k2);

Caused by:

Function evaluation failed while attempting to determine output size. The function might contain an

error, or might not be well-defined at the automatically-chosen point. To specify output size without

function evaluation, use 'OutputSize'.

>>

a=optimvar('a','Lower',-1,'Upper',+1);
b=optimvar('b','Lower',-1,'Upper',+1);
k1=optimvar('k1','LowerBound',-1,'UpperBound',1);
k2=optimvar('k1','LowerBound',-1,'UpperBound',1);
h=@(a,b,k1,k2)abs(a*exp(-j*k1*x)+b*exp(-j*k2*x));
hmax=@(a,b,k1,k2) max(h(a,b,k1,k2));
hmin=@(a,b,k1,k2) min(h(a,b,k1,k2));
cam=fcn2optimexpr( h, a,b,k1,k2);
camMax=fcn2optimexpr( hmax, a,b,k1,k2);
camMin=fcn2optimexpr( hmin, a,b,k1,k2);
prob = optimproblem("Objective",cam);
prob.Constraints.camUpper=camMax<=0.55;
prob.Constraints.camLower=camMin>=0.45;
[sol,fval] = solve(prob,"Solver","ga");

[Matt J]

Optimization variables cannot be combined with complex data.

This ran to completion for me:

a=optimvar('a','Lower',-1,'Upper',+1);
b=optimvar('b','Lower',-1,'Upper',+1);
k1=optimvar('k1','LowerBound',-1,'UpperBound',1);
k2=optimvar('k2','LowerBound',-1,'UpperBound',1);


x=linspace(0,10,1000);%<---- I made this up

h=@(a,b,k1,k2)abs(a*exp(-j*k1*x)+b*exp(-j*k2*x));
hmax=@(a,b,k1,k2) max(h(a,b,k1,k2));
hmin=@(a,b,k1,k2) min(h(a,b,k1,k2));

cam=fcn2optimexpr( h, a,b,k1,k2);
camMax=fcn2optimexpr( hmax, a,b,k1,k2);
camMin=fcn2optimexpr( hmin, a,b,k1,k2);

prob = optimproblem("Objective",camMax);
prob.Constraints.camUpper=camMax<=0.55;
prob.Constraints.camLower=camMin>=0.45;

[sol,fval] = solve(prob,"Solver","ga");

Solving problem using ga.
Optimization terminated: average change in the fitness value less than options.FunctionTolerance
 and constraint violation is less than options.ConstraintTolerance.

you have changed the original code.could you please use one "h" function?

No, you need multiple functions. However, here is a slightly different formulation which avoids hmin.

a=optimvar('a','Lower',-1,'Upper',+1);

b=optimvar('b','Lower',-1,'Upper',+1);

k1=optimvar('k1','LowerBound',-1,'UpperBound',1);

k2=optimvar('k2','LowerBound',-1,'UpperBound',1);

x=linspace(0,10,1000);%<---- I made this up

h=@(a,b,k1,k2)abs(a*exp(-j*k1*x)+b*exp(-j*k2*x));

hmax=@(a,b,k1,k2) max(h(a,b,k1,k2));

cam=fcn2optimexpr( h, a,b,k1,k2);

camMax=fcn2optimexpr( hmax, a,b,k1,k2);

prob = optimproblem("Objective",camMax);

prob.Constraints.camUpper=camMax<=0.55;

prob.Constraints.camLower=cam>=0.45;

[sol,fval] = solve(prob,"Solver","ga");